Peter, the two 16" discs you describe are included in the Doris Day Definitive Discography. As far as I know the song "Oops" is the only Doris Day recording on that disc, and it very likely the same version as was released commercially. The Capitol disc is quite rare. I have it in my collection. Accoustic Resarch (AR) used to produce a turntable that barely accommodated a 16" disc. I believe the turntable was an AR-5. The only other solution to playing the discs is through the equipment disc jockeys have at radio stations. Hope this helps.
Happy Days, Texas Gonzalo

Thank you for your reply, the 16 inch records weren't used in The Netherlands... so I have to find someone in The USA, I think who could help. Love to donate the record to anyone who can play it... and record it. If only through mobile phone the sound would be heard... so be it. So if anyone knows someone... let me know...

Peter, regarding the first new 16" disc you describe, the DDDDiscography had it listed as AFRS #108 dated 6 August 1944 as Fitch Band Wagon with two songs by Doris Day, as follows:
-- Amor (Doris Day and Gordon Drake) and -- Swingin' On A Star (Doris Day and Butch Stone). I will correct the numbering from 1108 to 108. I could not open the thread to the other two listings for some uinknown reason. Hope this helps. Happy Days, Texas Gonzalo